BAGHDAD, Iraq (CNN) -- Some 46,000 Iraqi refugees returned to their war-torn country last month, a sign of hope that the massive population flight since the 2003 U.S. invasion could be reversed, an Iraqi commander said Wednesday.

Iraqi refugees line up at the Iraq-Syria border in September.

Brig. Gen. Qassim Atta said he attributed the return to an improved security situation in Baghdad, where a crackdown has been in place since February.

"We are simply living in a better and obvious security situation," he said, citing the return of families to several Baghdad neighborhoods.

About 10,000 internally displaced families have gone back to their homes in the Iraqi capital, said Sattar Nawruz, spokesman for Iraq's Ministry of Displacement and Migration, also pointing to better security.

The Iraqi officials' assessments contrast with gloomy findings from the U.N. refugee agency and Iraqi Red Crescent Organization documenting an increase in displaced populations in recent months. The latter counted nearly 2.3 million internally displaced people in Iraq during September, a figure that has grown steadily this year.

In addition to the thousands of internally displaced people, more than 2.2 million Iraqis have fled to neighboring countries, mostly to Syria and Jordan, the U.N. refugee agency said. Those countries' social service agencies have been stretched by the presence of the refugees, and they have adopted tougher rules on the refugee flow.

Nawruz, who cited statistics that don't include the Kurdish region, said the number of Iraqi families internally displaced since February 2006 stands at 140,000, which amounts to at least 700,000 people since Iraqi families often average five to six people.

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He said "accurate data" indicates that forcible displacement in Baghdad has stopped in the past three months and ministry data indicates that 10,000 families have returned to their homes in the city since the start of the security plan in February.

Nawruz said Prime Minister Nuri al-Maliki ordered a grant of 1 million Iraqi dinars, about $700, to families returning to their homes. He said 3,231 families have received the money and more than 6,000 have applied for the funds.

The ministry on Tuesday started paying displaced families $120 per month for six months.

Nawruz attributes the differences in numbers between the Iraqi Red Crescent Organization and his ministry to dissimilar methods of data collection.

Iraqi Red Crescent President Said Ismail Hakki agreed the organizations' methods of data collection are different but stood by his group's figures.

In a report issued Sunday, Hakki's organization said that nearly 2.3 million people had been displaced by the end of September, a sharp increase from the August figure of 1.93 million and part of a steady rise this year.

"Children less than 12 years [old] comprised more than 65 percent of the total number. The majority of the displaced people [63.6 percent] were in Baghdad governorate," the report said.

The percentage of displaced people who are children has risen from 51.3 percent in August, the Iraqi Red Crescent Organization said.

Hakki attributed the increase to a "lack of services, lack of jobs and despair among the Iraqi people of the whole overall what's happening in Iraq." He said the displacement problem has persisted over the years but spiked with the February 2006 bombing of Al-Askariya Mosque in Samarra.

Baghdad and the Kurdish region were among the worst-hit areas, Hakki said, citing the deterioration of families and suffering of children, whose mothers have abandoned them in some cases "because they're becoming a liability."

He said he believes the "security situation in Iraq is improving at a very good speed" but adds that the lack of social services and jobs are factors in the displacement of people.

He said the increase in the number of displaced children presents new challenges for his organization, including problems of education and the trafficking of girls and boys alike.

"It's a social-economic problem. People are in despair now," Hakki said, adding that he hopes the Iraqi government will make improvements in jobs and social services to reverse the instability.E-mail to a friend